Selective Underfitting in Diffusion Models
This work provides insights into the generalization and performance of diffusion models, which are foundational for generative AI, but it is incremental as it refines existing perspectives on underfitting.
The paper tackles the question of which score diffusion models actually learn, proposing that better models selectively underfit the empirical score in certain regions of input space while approximating it accurately in others, and validates this through empirical interventions.
Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved question: which score do they actually learn? In principle, a diffusion model that matches the empirical score in the entire data space would simply reproduce the training data, failing to generate novel samples. Recent work addresses this question by arguing that diffusion models underfit the empirical score due to training-time inductive biases. In this work, we refine this perspective, introducing the notion of selective underfitting: instead of underfitting the score everywhere, better diffusion models more accurately approximate the score in certain regions of input space, while underfitting it in others. We characterize these regions and design empirical interventions to validate our perspective. Our results establish that selective underfitting is essential for understanding diffusion models, yielding new, testable insights into their generalization and generative performance.